##
##
##                    rubik3.mpl
##               simulates the moves of the 3x3 Rubik's cube
##
##                                         David Joyner, 1996
###########################################################

#libname:=`D:\\MAPLEV4/lib`,`D:\\MAPLEV4/share/games/gamehlp`;

A0:=matrix([[1,1,1,6,6,6,3,3,3],
 [1,1,1,6,6,6,3,3,3],
 [1,1,1,6,6,6,3,3,3],
 [2,2,2,5,5,5,4,4,4],
 [2,2,2,5,5,5,4,4,4],
 [2,2,2,5,5,5,4,4,4]]);


color1 := red;
color2 := blue;
color3 := coral;
color4 := plum;
color5 := green;
color6 := yellow;

rubik_squares := proc () 
local i; 
for i from 1 to 4 do 
F1.i:=[3,-3+2*(i-1),3];
F2.i:=[3,-3+2*(i-1),1];
F3.i:=[3,-3+2*(i-1),-1];
F4.i:=[3,-3+2*(i-1),-3];
R1.i:=[-3+2*(i-1),3,3];
R2.i:=[-3+2*(i-1),3,1];
R3.i:=[-3+2*(i-1),3,-1];
R4.i:=[-3+2*(i-1),3,-3];
B1.i:=[-3,-3+2*(i-1),3];
B2.i:=[-3,-3+2*(i-1),1];
B3.i:=[-3,-3+2*(i-1),-1];
B4.i:=[-3,-3+2*(i-1),-3];
L1.i:=[-3+2*(i-1),-3,3];
L2.i:=[-3+2*(i-1),-3,1];
L3.i:=[-3+2*(i-1),-3,-1];
L4.i:=[-3+2*(i-1),-3,-3];
U1.i:=[-3+2*(i-1),3,3];
U2.i:=[-3+2*(i-1),1,3];
U3.i:=[-3+2*(i-1),-1,3];
U4.i:=[-3+2*(i-1),-3,3];
D1.i:=[-3+2*(i-1),3,-3];
D2.i:=[-3+2*(i-1),1,-3];
D3.i:=[-3+2*(i-1),-1,-3];
D4.i:=[-3+2*(i-1),-3,-3];
od;
end;

cube_draw := proc (A::array) 
local i, j, 
face_F11,face_F12,face_F13,
face_F21,face_F22,face_F23,
face_F31,face_F32,face_F33,
face_B11,face_B12,face_B13,
face_B21,face_B22,face_B23,
face_B31,face_B32,face_B33,
face_U11,face_U12,face_U13,
face_U21,face_U22,face_U23,
face_U31,face_U32,face_U33,
face_R11,face_R12,face_R13,
face_R21,face_R22,face_R23,
face_R31,face_R32,face_R33,
face_L11,face_L12,face_L13,
face_L21,face_L22,face_L23,
face_L31,face_L32,face_L33, 
face_D11,face_D12,face_D13,
face_D21,face_D22,face_D23,
face_D31,face_D32,face_D33, L; 
rubik_squares();
face_F11:=polygonplot3d([F11,F12,F22,F21],style=patch,
color=color.(A[1,1]));
face_F12:=polygonplot3d([F12,F13,F23,F22],style=patch,
color=color.(A[1,2]));
face_F13:=polygonplot3d([F13,F14,F24,F23],style=patch,
color=color.(A[1,3]));
face_F21:=polygonplot3d([F21,F22,F32,F31],style=patch,
color=color.(A[2,1]));
face_F22:=polygonplot3d([F22,F23,F33,F32],style=patch,
color=color.(A[2,2]));
face_F23:=polygonplot3d([F23,F24,F34,F33],style=patch,
color=color.(A[2,3]));
face_F31:=polygonplot3d([F31,F32,F42,F41],style=patch,
color=color.(A[3,1]));
face_F32:=polygonplot3d([F32,F33,F43,F42],style=patch,
color=color.(A[3,2]));
face_F33:=polygonplot3d([F33,F34,F44,F43],style=patch,
color=color.(A[3,3]));
face_B11:=polygonplot3d([B11,B12,B22,B21],style=patch,
color=color.(A[1,7]));
face_B12:=polygonplot3d([B12,B13,B23,B22],style=patch,
color=color.(A[1,8]));
face_B13:=polygonplot3d([B13,B14,B24,B23],style=patch,
color=color.(A[1,9]));
face_B21:=polygonplot3d([B21,B22,B32,B31],style=patch,
color=color.(A[2,7]));
face_B22:=polygonplot3d([B22,B23,B33,B32],style=patch,
color=color.(A[2,8]));
face_B23:=polygonplot3d([B23,B24,B34,B33],style=patch,
color=color.(A[2,9]));
face_B31:=polygonplot3d([B31,B32,B42,B41],style=patch,
color=color.(A[3,7]));
face_B32:=polygonplot3d([B32,B33,B43,B42],style=patch,
color=color.(A[3,8]));
face_B33:=polygonplot3d([B33,B34,B44,B43],style=patch,
color=color.(A[3,9]));
face_U11:=polygonplot3d([U11,U12,U22,U21],style=patch,
color=color.(A[4,1]));
face_U21:=polygonplot3d([U12,U13,U23,U22],style=patch,
color=color.(A[4,2]));
face_U31:=polygonplot3d([U13,U14,U24,U23],style=patch,
color=color.(A[4,3]));
face_U12:=polygonplot3d([U21,U22,U32,U31],style=patch,
color=color.(A[5,1]));
face_U22:=polygonplot3d([U22,U23,U33,U32],style=patch,
color=color.(A[5,2]));
face_U32:=polygonplot3d([U23,U24,U34,U33],style=patch,
color=color.(A[5,3]));
face_U13:=polygonplot3d([U31,U32,U42,U41],style=patch,
color=color.(A[6,1]));
face_U23:=polygonplot3d([U32,U33,U43,U42],style=patch,
color=color.(A[6,2]));
face_U33:=polygonplot3d([U33,U34,U44,U43],style=patch,
color=color.(A[6,3]));
face_R11:=polygonplot3d([R11,R12,R22,R21],style=patch,
color=color.(A[1,4]));
face_R12:=polygonplot3d([R12,R13,R23,R22],style=patch,
color=color.(A[1,5]));
face_R13:=polygonplot3d([R13,R14,R24,R23],style=patch,
color=color.(A[1,6]));
face_R21:=polygonplot3d([R21,R22,R32,R31],style=patch,
color=color.(A[2,4]));
face_R22:=polygonplot3d([R22,R23,R33,R32],style=patch,
color=color.(A[2,5]));
face_R23:=polygonplot3d([R23,R24,R34,R33],style=patch,
color=color.(A[2,6]));
face_R31:=polygonplot3d([R31,R32,R42,R41],style=patch,
color=color.(A[3,4]));
face_R32:=polygonplot3d([R32,R33,R43,R42],style=patch,
color=color.(A[3,5]));
face_R33:=polygonplot3d([R33,R34,R44,R43],style=patch,
color=color.(A[3,6]));
face_L11:=polygonplot3d([L11,L12,L22,L21],style=patch,
color=color.(A[4,4]));
face_L12:=polygonplot3d([L12,L13,L23,L22],style=patch,
color=color.(A[4,5]));
face_L13:=polygonplot3d([L13,L14,L24,L23],style=patch,
color=color.(A[4,6]));
face_L21:=polygonplot3d([L21,L22,L32,L31],style=patch,
color=color.(A[5,4]));
face_L22:=polygonplot3d([L22,L23,L33,L32],style=patch,
color=color.(A[5,5]));
face_L23:=polygonplot3d([L23,L24,L34,L33],style=patch,
color=color.(A[5,6]));
face_L31:=polygonplot3d([L31,L32,L42,L41],style=patch,
color=color.(A[6,4]));
face_L32:=polygonplot3d([L32,L33,L43,L42],style=patch,
color=color.(A[6,5]));
face_L33:=polygonplot3d([L33,L34,L44,L43],style=patch,
color=color.(A[6,6]));
face_D11:=polygonplot3d([D11,D12,D22,D21],style=patch,
color=color.(A[4,7]));
face_D21:=polygonplot3d([D12,D13,D23,D22],style=patch,
color=color.(A[4,8]));
face_D31:=polygonplot3d([D13,D14,D24,D23],style=patch,
color=color.(A[4,9]));
face_D12:=polygonplot3d([D21,D22,D32,D31],style=patch,
color=color.(A[5,7]));
face_D22:=polygonplot3d([D22,D23,D33,D32],style=patch,
color=color.(A[5,8]));
face_D32:=polygonplot3d([D23,D24,D34,D33],style=patch,
color=color.(A[5,9]));
face_D13:=polygonplot3d([D31,D32,D42,D41],style=patch,
color=color.(A[6,7]));
face_D23:=polygonplot3d([D32,D33,D43,D42],style=patch,
color=color.(A[6,8]));
face_D33:=polygonplot3d([D33,D34,D44,D43],style=patch,
color=color.(A[6,9]));
L:= [face_F11,face_F12,face_F13,
face_F21,face_F22,face_F23,
face_F31,face_F32,face_F33,
face_B11,face_B12,face_B13,
face_B21,face_B22,face_B23,
face_B31,face_B32,face_B33,
face_U11,face_U12,face_U13,
face_U21,face_U22,face_U23,
face_U31,face_U32,face_U33,
face_R11,face_R12,face_R13,
face_R21,face_R22,face_R23,
face_R31,face_R32,face_R33,
face_L11,face_L12,face_L13,
face_L21,face_L22,face_L23,
face_L31,face_L32,face_L33,
face_D11,face_D12,face_D13,
face_D21,face_D22,face_D23,
face_D31,face_D32,face_D33]; 
RETURN(L) 
end;

move_r := proc (A) 
local j, k, AA,indices; 
AA := matrix(6,9); 
indices:={[1,3],[2,3],[3,3],[4,3],[4,2],[4,1],[1,9],
[2,9],[3,9],[4,9],[4,8],[4,7],[1,4],[1,6],[3,6],
[3,4],[1,5],[2,6],[3,5],[2,4]};
AA[4,3]:=A[3,3]; 
AA[4,2]:=A[2,3];
AA[4,1]:=A[1,3]; #front to up
AA[1,9]:=A[4,3];
AA[2,9]:=A[4,2]; 
AA[3,9]:=A[4,1]; #up to back
AA[4,9]:=A[3,9];
AA[4,8]:=A[2,9]; 
AA[4,7]:=A[1,9]; #back to down
AA[3,3]:=A[4,7];
AA[2,3]:=A[4,8]; 
AA[1,3]:=A[4,9]; #up to back
AA[1,4]:=A[1,6];
AA[1,6]:=A[3,6];
AA[3,6]:=A[3,4];
AA[3,4]:=A[1,4];
AA[1,5]:=A[2,6];
AA[2,6]:=A[3,5];
AA[3,5]:=A[2,4];
AA[2,4]:=A[1,5];
for j from 1 to 6 do
 for k from 1 to 9 do
  if not(member([j,k],indices)) then
   AA[j,k]:=A[j,k] 
  fi;
 od;
od;
RETURN(AA) 
end; #move_r

move_u := proc (A) 
local j, k, AA,indices; 
AA := matrix(6,9); 
indices:={[1,1],[1,2],[1,3],[1,4],[1,5],[1,6],[1,7],
[1,8],[1,9],[4,4],[4,5],[4,6],[6,1],[6,3],[4,3],
[4,1],[6,2],[5,3],[4,2],[5,1]};
AA[1,6]:=A[1,9]; 
AA[1,5]:=A[1,8];
AA[1,4]:=A[1,7]; #front to right
AA[1,9]:=A[4,4];
AA[1,8]:=A[4,5]; 
AA[1,7]:=A[4,6]; #back to right
AA[4,6]:=A[1,3];
AA[4,5]:=A[1,2]; 
AA[4,4]:=A[1,1]; #back to down
AA[1,1]:=A[1,6];
AA[1,2]:=A[1,5]; 
AA[1,3]:=A[1,4]; #up to back
AA[4,1]:=A[6,1];
AA[6,1]:=A[6,3];
AA[6,3]:=A[4,3];
AA[4,3]:=A[4,1];
AA[6,2]:=A[5,3];
AA[5,3]:=A[4,2];
AA[4,2]:=A[5,1];
AA[5,1]:=A[6,2];
for j from 1 to 6 do
 for k from 1 to 9 do
  if not(member([j,k],indices)) then
   AA[j,k]:=A[j,k] 
  fi;
 od;
od;
RETURN(AA) 
end; #move_u

move_l := proc (A) 
local j, k, AA,indices; 
AA := matrix(6,9); 
indices:={[1,1],[2,1],[3,1],[1,7],[2,7],[3,7],[6,7],
[6,8],[6,9],[6,1],[6,2],[6,3],[4,4],[6,4],[6,6],[4,6],
[4,5],[5,4],[6,5],[5,6]};
AA[1,1]:=A[6,1]; 
AA[2,1]:=A[6,2];
AA[3,1]:=A[6,3]; #front to up
AA[6,7]:=A[3,1];
AA[6,8]:=A[2,1]; 
AA[6,9]:=A[1,1]; #back to up
AA[1,7]:=A[6,7];
AA[2,7]:=A[6,8]; 
AA[3,7]:=A[6,9]; #back to down
AA[6,1]:=A[3,7];
AA[6,2]:=A[2,7]; 
AA[6,3]:=A[1,7]; #up to back
AA[6,4]:=A[6,6];
AA[4,4]:=A[6,4];
AA[4,6]:=A[4,4];
AA[6,6]:=A[4,6];
AA[5,4]:=A[6,5];
AA[6,5]:=A[5,6];
AA[5,6]:=A[4,5];
AA[4,5]:=A[5,4];
for j from 1 to 6 do
 for k from 1 to 9 do
  if not(member([j,k],indices)) then
   AA[j,k]:=A[j,k] 
  fi;
 od;
od;
RETURN(AA) 
end; #move_l

move_f := proc (A) 
local j, k, AA,indices; 
AA := matrix(6,9); 
indices:={[1,6],[2,6],[3,6],[4,9],[5,9],[6,9],[6,6],
[5,6],[4,6],[6,3],[5,3],[4,3],[1,1],[3,1],
[3,3],[1,3],[1,2],[2,1],[3,2],[2,3]};
AA[1,1]:=A[3,1];
AA[3,1]:=A[3,3];
AA[3,3]:=A[1,3];
AA[1,3]:=A[1,1];
AA[1,2]:=A[2,1];
AA[2,1]:=A[3,2];
AA[3,2]:=A[2,3];
AA[2,3]:=A[1,2];
AA[1,6]:=A[6,3]; 
AA[2,6]:=A[5,3];
AA[3,6]:=A[4,3]; #up to rear
AA[4,9]:=A[1,6];
AA[5,9]:=A[2,6]; 
AA[6,9]:=A[3,6]; #rear to down
AA[6,6]:=A[4,9];
AA[5,6]:=A[5,9]; 
AA[4,6]:=A[6,9]; #down to left
AA[6,3]:=A[6,6];
AA[5,3]:=A[5,6]; 
AA[4,3]:=A[4,6]; #left to up
for j from 1 to 6 do
 for k from 1 to 9 do
  if not(member([j,k],indices)) then
   AA[j,k]:=A[j,k] 
  fi;
 od;
od;
RETURN(AA) 
end; #move_f

move_b := proc (A) 
local j, k, AA,indices; 
AA := matrix(6,9); 
indices:={[4,1],[5,1],[6,1],[6,4],[5,4],
[4,4],[4,7],[5,7],[6,7],[3,4],
[2,4],[1,4],[1,8],[1,9],[1,7],
[2,9],[2,7],[3,7],[3,9],[3,8]};
AA[1,8]:=A[2,9];
AA[2,9]:=A[3,8];
AA[3,8]:=A[2,7];
AA[2,7]:=A[1,8];
AA[1,9]:=A[3,9];
AA[3,9]:=A[3,7];
AA[3,7]:=A[1,7];
AA[1,7]:=A[1,9];
AA[4,1]:=A[3,4]; 
AA[5,1]:=A[2,4];
AA[6,1]:=A[1,4]; #right to up
AA[6,4]:=A[6,1];
AA[5,4]:=A[5,1]; 
AA[4,4]:=A[4,1]; #up to left
AA[4,7]:=A[6,4];
AA[5,7]:=A[5,4]; 
AA[6,7]:=A[4,4]; #down to left
AA[3,4]:=A[6,7];
AA[2,4]:=A[5,7]; 
AA[1,4]:=A[4,7]; #left to up
for j from 1 to 6 do
 for k from 1 to 9 do
  if not(member([j,k],indices)) then
   AA[j,k]:=A[j,k] 
  fi;
 od;
od;
RETURN(AA) 
end; #move_b

move_d := proc (A) 
local j, k, AA,indices; 
AA := matrix(6,9); 
indices:={[3,6],[3,5],[3,4],[3,9],[3,8],[3,7],[6,4],
[6,5],[6,6],[3,1],[3,2],[3,3],[6,9],[6,7],[4,7],[4,9],
[5,9],[6,8],[5,7],[4,8]};
AA[6,9]:=A[6,7];
AA[6,7]:=A[4,7];
AA[4,7]:=A[4,9];
AA[4,9]:=A[6,9];
AA[5,9]:=A[6,8];
AA[6,8]:=A[5,7];
AA[5,7]:=A[4,8];
AA[4,8]:=A[5,9];
AA[3,6]:=A[3,1]; 
AA[3,5]:=A[3,2];
AA[3,4]:=A[3,3]; #front to right
AA[3,9]:=A[3,6];
AA[3,8]:=A[3,5]; 
AA[3,7]:=A[3,4]; #up to left
AA[6,4]:=A[3,9];
AA[6,5]:=A[3,8]; 
AA[6,6]:=A[3,7]; #down to left
AA[3,1]:=A[6,4];
AA[3,2]:=A[6,5]; 
AA[3,3]:=A[6,6]; #left to up
for j from 1 to 6 do
 for k from 1 to 9 do
  if not(member([j,k],indices)) then
   AA[j,k]:=A[j,k] 
  fi;
 od;
od;
RETURN(AA) 
end; #move_d

move_power:=proc(g,A)
local i,j,AA,generators,gen,power;
generators:={R,U,F,D,L,B};
AA:=A;
if type(g,`^`) then 
  gen:=op(1,g);
  power:=op(2,g) mod 4;
 else if member(g,generators) then 
   gen:=g;
   power:=1;
 fi;
fi;
if g=1 then RETURN(AA); fi;
for i from 1 to power do
 if gen=R then AA:=move_r(AA) fi;
 if gen=L then AA:=move_l(AA) fi;
 if gen=U then AA:=move_u(AA) fi;
 if gen=D then AA:=move_d(AA) fi;
 if gen=F then AA:=move_f(AA) fi;
 if gen=B then AA:=move_b(AA) fi;
od;
RETURN(AA);
end;

move:=proc(w,A)
local i,AA,generators;
generators:={R,U,F,D,L,B};
AA:=A;
if type(w,`^`) then 
  AA:=move_power(w,AA);
fi;
if w=1 then RETURN(AA); fi;
if member(w,generators) then
  AA:=move_power(w,AA);
fi;
if type(w,list) then 
 for i from 1 to nops(w) do
   AA:=move_power(op(i,w),AA);
 od;
fi;
RETURN(AA);
end;

rc := proc (L, A) local AA, LL; 
AA := move(L,A); LL := cube_draw(AA); 
display3d(LL) end;